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In statistical physics, The calculation of partition function for an ensemble takes a Boltzmann's distribution of the Hamiltonian. Similarly, In Monte-Carlo integration of Molecular Dynamics simulation, The Boltzmann distribution is used to update the configuration of each particle. The essence of my question is that why do we assume that the Hamiltonian follows the Bolzmann's distribution and not any other probability distribution for that matter?

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    $\begingroup$ Because the Boltzmann distribution gives the probability of finding the system in any given state, assuming thermodynamic equilibrium... $\endgroup$ – lemon Jul 27 '18 at 10:47

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